Endoscopy and cohomology growth on unitary groups

Abstract: One of the principles of the endoscopic classification is that if an automorphic representation of a classical group is non-tempered at any place, then it should arise as a transfer from an endoscopic subgroup. One also knows that any representation of a unitary group that contributes to the cohomology of the associated symmetric space outside of middle degree must be non-tempered at infinity. By combining these two ideas, I will derive conjecturally sharp upper bounds for the growth of Betti numbers in congruence towers of complex hyperbolic manifolds. This is joint work with Sug Woo Shin.

Date

Affiliation

University of Wisconsin; Member, School of Mathematics

Speakers

Simon Marshall